<!DOCTYPE html>
<html lang="zh" dir="ltr" class="client-nojs">
<head>
<title>std::ratio</title>
<meta charset="UTF-8">
<meta name="generator" content="MediaWiki 1.21.2">
<link rel="shortcut icon" href="../../../../common/favicon.ico">
<link rel="stylesheet" href="../../../../common/ext.css">
<meta name="ResourceLoaderDynamicStyles" content="">
<link rel="stylesheet" href="../../../../common/site_modules.css">
<style>a:lang(ar),a:lang(ckb),a:lang(fa),a:lang(kk-arab),a:lang(mzn),a:lang(ps),a:lang(ur){text-decoration:none}#toc{display:none}.editsection{display:none}
/* cache key: mwiki1-mwiki_zh_:resourceloader:filter:minify-css:7:15cea3ec788a65b5187d4018eed543bf */</style>

<script src="../../../../common/startup_scripts.js"></script>
<script>if(window.mw){
mw.config.set({"wgCanonicalNamespace":"","wgCanonicalSpecialPageName":false,"wgNamespaceNumber":0,"wgPageName":"cpp/numeric/ratio/ratio","wgTitle":"cpp/numeric/ratio/ratio","wgCurRevisionId":62827,"wgArticleId":3430,"wgIsArticle":true,"wgAction":"view","wgUserName":null,"wgUserGroups":["*"],"wgCategories":[],"wgBreakFrames":false,"wgPageContentLanguage":"zh","wgSeparatorTransformTable":["",""],"wgDigitTransformTable":["",""],"wgDefaultDateFormat":"zh","wgMonthNames":["","1月","2月","3月","4月","5月","6月","7月","8月","9月","10月","11月","12月"],"wgMonthNamesShort":["","1月","2月","3月","4月","5月","6月","7月","8月","9月","10月","11月","12月"],"wgRelevantPageName":"cpp/numeric/ratio/ratio","wgUserVariant":"zh","wgRestrictionEdit":[],"wgRestrictionMove":[]});
}</script><script>if(window.mw){
mw.loader.implement("user.options",function(){mw.user.options.set({"ccmeonemails":0,"cols":80,"date":"default","diffonly":0,"disablemail":0,"disablesuggest":0,"editfont":"default","editondblclick":0,"editsection":0,"editsectiononrightclick":0,"enotifminoredits":0,"enotifrevealaddr":0,"enotifusertalkpages":1,"enotifwatchlistpages":0,"extendwatchlist":0,"externaldiff":0,"externaleditor":0,"fancysig":0,"forceeditsummary":0,"gender":"unknown","hideminor":0,"hidepatrolled":0,"imagesize":2,"justify":0,"math":1,"minordefault":0,"newpageshidepatrolled":0,"nocache":0,"noconvertlink":0,"norollbackdiff":0,"numberheadings":0,"previewonfirst":0,"previewontop":1,"quickbar":5,"rcdays":7,"rclimit":50,"rememberpassword":0,"rows":25,"searchlimit":20,"showhiddencats":0,"showjumplinks":1,"shownumberswatching":1,"showtoc":0,"showtoolbar":1,"skin":"cppreference2","stubthreshold":0,"thumbsize":2,"underline":2,"uselivepreview":0,"usenewrc":0,"watchcreations":0,"watchdefault":0,"watchdeletion":0,
"watchlistdays":3,"watchlisthideanons":0,"watchlisthidebots":0,"watchlisthideliu":0,"watchlisthideminor":0,"watchlisthideown":0,"watchlisthidepatrolled":0,"watchmoves":0,"wllimit":250,"variant":"zh","language":"zh","searchNs0":true,"searchNs1":false,"searchNs2":false,"searchNs3":false,"searchNs4":false,"searchNs5":false,"searchNs6":false,"searchNs7":false,"searchNs8":false,"searchNs9":false,"searchNs10":false,"searchNs11":false,"searchNs12":false,"searchNs13":false,"searchNs14":false,"searchNs15":false,"gadget-MathJax":1,"gadget-ColiruCompiler":1});;},{},{});mw.loader.implement("user.tokens",function(){mw.user.tokens.set({"editToken":"+\\","patrolToken":false,"watchToken":false});;},{},{});
/* cache key: mwiki1-mwiki_zh_:resourceloader:filter:minify-js:7:258d7cd6aa9aa67dee25e01fb6a9e505 */
}</script>
<script>if(window.mw){
mw.loader.load(["mediawiki.page.startup","mediawiki.legacy.wikibits","mediawiki.legacy.ajax"]);
}</script>
<style type="text/css">/*<![CDATA[*/
.source-cpp {line-height: normal;}
.source-cpp li, .source-cpp pre {
	line-height: normal; border: 0px none white;
}
/**
 * GeSHi Dynamically Generated Stylesheet
 * --------------------------------------
 * Dynamically generated stylesheet for cpp
 * CSS class: source-cpp, CSS id: 
 * GeSHi (C) 2004 - 2007 Nigel McNie, 2007 - 2008 Benny Baumann
 * (http://qbnz.com/highlighter/ and http://geshi.org/)
 * --------------------------------------
 */
.cpp.source-cpp .de1, .cpp.source-cpp .de2 {font: normal normal 1em/1.2em monospace; margin:0; padding:0; background:none; vertical-align:top;}
.cpp.source-cpp  {font-family:monospace;}
.cpp.source-cpp .imp {font-weight: bold; color: red;}
.cpp.source-cpp li, .cpp.source-cpp .li1 {font-weight: normal; vertical-align:top;}
.cpp.source-cpp .ln {width:1px;text-align:right;margin:0;padding:0 2px;vertical-align:top;}
.cpp.source-cpp .li2 {font-weight: bold; vertical-align:top;}
.cpp.source-cpp .kw1 {color: #0000dd;}
.cpp.source-cpp .kw2 {color: #0000ff;}
.cpp.source-cpp .kw3 {color: #0000dd;}
.cpp.source-cpp .kw4 {color: #0000ff;}
.cpp.source-cpp .co1 {color: #909090;}
.cpp.source-cpp .co2 {color: #339900;}
.cpp.source-cpp .coMULTI {color: #ff0000; font-style: italic;}
.cpp.source-cpp .es0 {color: #008000; font-weight: bold;}
.cpp.source-cpp .es1 {color: #008000; font-weight: bold;}
.cpp.source-cpp .es2 {color: #008000; font-weight: bold;}
.cpp.source-cpp .es3 {color: #008000; font-weight: bold;}
.cpp.source-cpp .es4 {color: #008000; font-weight: bold;}
.cpp.source-cpp .es5 {color: #008000; font-weight: bold;}
.cpp.source-cpp .br0 {color: #008000;}
.cpp.source-cpp .sy0 {color: #008000;}
.cpp.source-cpp .sy1 {color: #000080;}
.cpp.source-cpp .sy2 {color: #000040;}
.cpp.source-cpp .sy3 {color: #000040;}
.cpp.source-cpp .sy4 {color: #008080;}
.cpp.source-cpp .st0 {color: #008000;}
.cpp.source-cpp .nu0 {color: #000080;}
.cpp.source-cpp .nu6 {color: #000080;}
.cpp.source-cpp .nu8 {color: #000080;}
.cpp.source-cpp .nu12 {color: #000080;}
.cpp.source-cpp .nu16 {color:#000080;}
.cpp.source-cpp .nu17 {color:#000080;}
.cpp.source-cpp .nu18 {color:#000080;}
.cpp.source-cpp .nu19 {color:#000080;}
.cpp.source-cpp .ln-xtra, .cpp.source-cpp li.ln-xtra, .cpp.source-cpp div.ln-xtra {background-color: #ffc;}
.cpp.source-cpp span.xtra { display:block; }

/*]]>*/
</style><!--[if lt IE 7]><style type="text/css">body{behavior:url("/mwiki/skins/cppreference2/csshover.min.htc")}</style><![endif]--></head>
<body class="mediawiki ltr sitedir-ltr ns-0 ns-subject page-cpp_numeric_ratio_ratio skin-cppreference2 action-view cpp-navbar">
        <!-- header -->
        <!-- /header -->
        <!-- content -->
<div id="cpp-content-base">
            <div id="content">
                <a id="top"></a>
                <div id="mw-js-message" style="display:none;"></div>
                                <!-- firstHeading -->
<h1 id="firstHeading" class="firstHeading"><span style="font-size:0.7em; line-height:130%">std::</span>ratio</h1>
                <!-- /firstHeading -->
                <!-- bodyContent -->
                <div id="bodyContent">
                                        <!-- tagline -->
                    <div id="siteSub">来自cppreference.com</div>
                    <!-- /tagline -->
                                        <!-- subtitle -->
                    <div id="contentSub"><span class="subpages">&lt; <a href="../../../cpp.html" title="cpp">cpp</a>‎ | <a href="../../numeric.html" title="cpp/numeric">numeric</a>‎ | <a href="../ratio.html" title="cpp/numeric/ratio">ratio</a></span></div>
                    <!-- /subtitle -->
                                                            <!-- bodycontent -->
                    <div id="mw-content-text" lang="zh" dir="ltr" class="mw-content-ltr"><div class="t-navbar" style=""><div class="t-navbar-sep"> </div><div class="t-navbar-head"><a href="../../../cpp.html" title="cpp"> C++</a><div class="t-navbar-menu"><div><div><table class="t-nv-begin" cellpadding="0" style="line-height:1.1em;">
<tr class="t-nv"><td colspan="5"> <a href="../../language.html" title="cpp/language">语言</a> </td></tr>
<tr class="t-nv"><td colspan="5"> <a href="../../header.html" title="cpp/header">标准库头文件</a> </td></tr>
<tr class="t-nv"><td colspan="5"> <a href="../../freestanding.html" title="cpp/freestanding"> 自立与有宿主实现</a> </td></tr>
<tr class="t-nv"><td colspan="5"> <a href="../../named_req.html" title="cpp/named req">具名要求</a> </td></tr>
<tr class="t-nv"><td colspan="5"> <a href="../../utility.html#.E8.AF.AD.E8.A8.80.E6.94.AF.E6.8C.81" title="cpp/utility">语言支持库</a> </td></tr>
<tr class="t-nv"><td colspan="5"> <a href="../../concepts.html" title="cpp/concepts">概念库</a> <span class="t-mark-rev t-since-cxx20">(C++20)</span> </td></tr>
<tr class="t-nv"><td colspan="5"> <a href="../../error.html" title="cpp/error">诊断库</a> </td></tr>
<tr class="t-nv"><td colspan="5"> <a href="../../utility.html" title="cpp/utility">工具库</a> </td></tr>
<tr class="t-nv"><td colspan="5"> <a href="../../string.html" title="cpp/string">字符串库</a> </td></tr>
<tr class="t-nv"><td colspan="5"> <a href="https://zh.cppreference.com/w/cpp/container" title="cpp/container">容器库</a> </td></tr>
<tr class="t-nv"><td colspan="5"> <a href="../../iterator.html" title="cpp/iterator">迭代器库</a> </td></tr>
<tr class="t-nv"><td colspan="5"> <a href="../../ranges.html" title="cpp/ranges"> 范围库</a> <span class="t-mark-rev t-since-cxx20">(C++20)</span> </td></tr>
<tr class="t-nv"><td colspan="5"> <a href="../../algorithm.html" title="cpp/algorithm">算法库</a> </td></tr>
<tr class="t-nv"><td colspan="5"> <a href="../../numeric.html" title="cpp/numeric">数值库</a> </td></tr>
<tr class="t-nv"><td colspan="5"> <a href="../../io.html" title="cpp/io">输入/输出库</a> </td></tr>
<tr class="t-nv"><td colspan="5"> <a href="../../locale.html" title="cpp/locale">本地化库</a> </td></tr>
<tr class="t-nv"><td colspan="5"> <a href="../../regex.html" title="cpp/regex">正则表达式库</a> <span class="t-mark-rev t-since-cxx11">(C++11)</span> </td></tr>
<tr class="t-nv"><td colspan="5"> <a href="../../atomic.html" title="cpp/atomic">原子操作库</a> <span class="t-mark-rev t-since-cxx11">(C++11)</span> </td></tr>
<tr class="t-nv"><td colspan="5"> <a href="../../thread.html" title="cpp/thread">线程支持库</a> <span class="t-mark-rev t-since-cxx11">(C++11)</span> </td></tr>
<tr class="t-nv"><td colspan="5"> <a href="../../filesystem.html" title="cpp/filesystem">文件系统库</a> <span class="t-mark-rev t-since-cxx17">(C++17)</span> </td></tr>
<tr class="t-nv"><td colspan="5"> <a href="../../experimental.html" title="cpp/experimental">技术规范</a> </td></tr>
</table></div><div></div></div></div></div><div class="t-navbar-sep"> </div><div class="t-navbar-head"><a href="../../numeric.html" title="cpp/numeric">数值库</a><div class="t-navbar-menu"><div><div><table class="t-nv-begin" cellpadding="0" style="">
<tr class="t-nv"><td colspan="5"> <a href="../math.html" title="cpp/numeric/math">常用数学函数</a> </td></tr>
<tr class="t-nv"><td colspan="5"> <a href="../special_functions.html" title="cpp/numeric/special functions">数学特殊函数</a> <span class="t-mark-rev t-since-cxx17">(C++17)</span> </td></tr>
<tr class="t-nv"><td colspan="5"> <a href="../constants.html" title="cpp/numeric/constants">数学常数</a> <span class="t-mark-rev t-since-cxx20">(C++20)</span></td></tr>
<tr class="t-nv"><td colspan="5"> <a href="../fenv.html" title="cpp/numeric/fenv">浮点环境</a> <span class="t-mark-rev t-since-cxx11">(C++11)</span> </td></tr>
<tr class="t-nv"><td colspan="5"> <a href="../complex.html" title="cpp/numeric/complex">复数</a> </td></tr>
<tr class="t-nv"><td colspan="5"> <a href="../valarray.html" title="cpp/numeric/valarray">数值数组</a> </td></tr>
<tr class="t-nv"><td colspan="5"> <a href="../random.html" title="cpp/numeric/random">伪随机数生成</a> </td></tr>
<tr class="t-nv"><td colspan="5"> <a href="../ratio.html" title="cpp/numeric/ratio">编译时有理数算术</a> <span class="t-mark-rev t-since-cxx11">(C++11)</span> </td></tr>
<tr class="t-nv-h2"><td colspan="5">数值算法</td></tr>
<tr class="t-nv"><td colspan="5"><div class="t-nv-ln-table"><div><a href="../gcd.html" title="cpp/numeric/gcd"><span class="t-lines"><span>gcd</span></span></a></div><div><span class="t-lines"><span><span class="t-mark-rev t-since-cxx17">(C++17)</span></span></span></div></div></td></tr>
<tr class="t-nv"><td colspan="5"><div class="t-nv-ln-table"><div><a href="../lcm.html" title="cpp/numeric/lcm"><span class="t-lines"><span>lcm</span></span></a></div><div><span class="t-lines"><span><span class="t-mark-rev t-since-cxx17">(C++17)</span></span></span></div></div></td></tr>
<tr class="t-nv-h2"><td colspan="5">插值</td></tr>
<tr class="t-nv"><td colspan="5"><div class="t-nv-ln-table"><div><a href="../midpoint.html" title="cpp/numeric/midpoint"><span class="t-lines"><span>midpoint</span></span></a></div><div><span class="t-lines"><span><span class="t-mark-rev t-since-cxx20">(C++20)</span></span></span></div></div></td></tr>
<tr class="t-nv"><td colspan="5"><div class="t-nv-ln-table"><div><a href="../lerp.html" title="cpp/numeric/lerp"><span class="t-lines"><span>lerp</span></span></a></div><div><span class="t-lines"><span><span class="t-mark-rev t-since-cxx20">(C++20)</span></span></span></div></div></td></tr>
<tr class="t-nv-h2"><td colspan="5">通用数值运算</td></tr>
<tr class="t-nv"><td colspan="5"><div class="t-nv-ln-table"><div><a href="../../algorithm/iota.html" title="cpp/algorithm/iota"><span class="t-lines"><span>iota</span></span></a></div><div><span class="t-lines"><span><span class="t-mark-rev t-since-cxx11">(C++11)</span></span></span></div></div></td></tr>
<tr class="t-nv"><td colspan="5"><div class="t-nv-ln-table"><div><a href="../../algorithm/accumulate.html" title="cpp/algorithm/accumulate"><span class="t-lines"><span>accumulate</span></span></a></div></div></td></tr>
<tr class="t-nv"><td colspan="5"><div class="t-nv-ln-table"><div><a href="../../algorithm/inner_product.html" title="cpp/algorithm/inner product"><span class="t-lines"><span>inner_product</span></span></a></div></div></td></tr>
<tr class="t-nv"><td colspan="5"><div class="t-nv-ln-table"><div><a href="../../algorithm/adjacent_difference.html" title="cpp/algorithm/adjacent difference"><span class="t-lines"><span>adjacent_difference</span></span></a></div></div></td></tr>
<tr class="t-nv"><td colspan="5"><div class="t-nv-ln-table"><div><a href="../../algorithm/partial_sum.html" title="cpp/algorithm/partial sum"><span class="t-lines"><span>partial_sum</span></span></a></div></div></td></tr>
<tr class="t-nv-h2"><td colspan="5">位操作</td></tr>
<tr class="t-nv"><td colspan="5"><div class="t-nv-ln-table"><div><a href="../bit_cast.html" title="cpp/numeric/bit cast"><span class="t-lines"><span>bit_cast</span></span></a></div><div><span class="t-lines"><span><span class="t-mark-rev t-since-cxx20">(C++20)</span></span></span></div></div></td></tr>
<tr class="t-nv"><td colspan="5"><div class="t-nv-ln-table"><div><a href="../has_single_bit.html" title="cpp/numeric/has single bit"><span class="t-lines"><span>has_single_bit</span></span></a></div><div><span class="t-lines"><span><span class="t-mark-rev t-since-cxx20">(C++20)</span></span></span></div></div></td></tr>
<tr class="t-nv"><td colspan="5"><div class="t-nv-ln-table"><div><a href="../bit_ceil.html" title="cpp/numeric/bit ceil"><span class="t-lines"><span>bit_ceil</span></span></a></div><div><span class="t-lines"><span><span class="t-mark-rev t-since-cxx20">(C++20)</span></span></span></div></div></td></tr>
<tr class="t-nv"><td colspan="5"><div class="t-nv-ln-table"><div><a href="../bit_floor.html" title="cpp/numeric/bit floor"><span class="t-lines"><span>bit_floor</span></span></a></div><div><span class="t-lines"><span><span class="t-mark-rev t-since-cxx20">(C++20)</span></span></span></div></div></td></tr>
<tr class="t-nv"><td colspan="5"><div class="t-nv-ln-table"><div><a href="../bit_width.html" title="cpp/numeric/bit width"><span class="t-lines"><span>bit_width</span></span></a></div><div><span class="t-lines"><span><span class="t-mark-rev t-since-cxx20">(C++20)</span></span></span></div></div></td></tr>
<tr class="t-nv"><td colspan="5"><div class="t-nv-ln-table"><div><a href="../rotl.html" title="cpp/numeric/rotl"><span class="t-lines"><span>rotl</span></span></a></div><div><span class="t-lines"><span><span class="t-mark-rev t-since-cxx20">(C++20)</span></span></span></div></div></td></tr>
<tr class="t-nv"><td colspan="5"><div class="t-nv-ln-table"><div><a href="../rotr.html" title="cpp/numeric/rotr"><span class="t-lines"><span>rotr</span></span></a></div><div><span class="t-lines"><span><span class="t-mark-rev t-since-cxx20">(C++20)</span></span></span></div></div></td></tr>
<tr class="t-nv"><td colspan="5"><div class="t-nv-ln-table"><div><a href="../countl_zero.html" title="cpp/numeric/countl zero"><span class="t-lines"><span>countl_zero</span></span></a></div><div><span class="t-lines"><span><span class="t-mark-rev t-since-cxx20">(C++20)</span></span></span></div></div></td></tr>
<tr class="t-nv"><td colspan="5"><div class="t-nv-ln-table"><div><a href="../countl_one.html" title="cpp/numeric/countl one"><span class="t-lines"><span>countl_one</span></span></a></div><div><span class="t-lines"><span><span class="t-mark-rev t-since-cxx20">(C++20)</span></span></span></div></div></td></tr>
<tr class="t-nv"><td colspan="5"><div class="t-nv-ln-table"><div><a href="../countr_zero.html" title="cpp/numeric/countr zero"><span class="t-lines"><span>countr_zero</span></span></a></div><div><span class="t-lines"><span><span class="t-mark-rev t-since-cxx20">(C++20)</span></span></span></div></div></td></tr>
<tr class="t-nv"><td colspan="5"><div class="t-nv-ln-table"><div><a href="../countr_one.html" title="cpp/numeric/countr one"><span class="t-lines"><span>countr_one</span></span></a></div><div><span class="t-lines"><span><span class="t-mark-rev t-since-cxx20">(C++20)</span></span></span></div></div></td></tr>
<tr class="t-nv"><td colspan="5"><div class="t-nv-ln-table"><div><a href="../popcount.html" title="cpp/numeric/popcount"><span class="t-lines"><span>popcount</span></span></a></div><div><span class="t-lines"><span><span class="t-mark-rev t-since-cxx20">(C++20)</span></span></span></div></div></td></tr>
<tr class="t-nv"><td colspan="5"><div class="t-nv-ln-table"><div><a href="../../types/endian.html" title="cpp/types/endian"><span class="t-lines"><span>endian</span></span></a></div><div><span class="t-lines"><span><span class="t-mark-rev t-since-cxx20">(C++20)</span></span></span></div></div></td></tr>
</table></div><div></div></div></div></div><div class="t-navbar-sep"> </div><div class="t-navbar-head"><a href="../ratio.html" title="cpp/numeric/ratio">编译时有理数算术</a><div class="t-navbar-menu"><div><div><table class="t-nv-begin" cellpadding="0" style="">
<tr class="t-nv"><td colspan="5"><div class="t-nv-ln-table"><div><strong class="selflink"><span class="t-lines"><span>ratio</span></span></strong></div><div><span class="t-lines"><span><span class="t-mark-rev t-since-cxx11">(C++11)</span></span></span></div></div></td></tr>
<tr class="t-nv-h2"><td colspan="5"> 算术</td></tr>
<tr class="t-nv"><td colspan="5"><div class="t-nv-ln-table"><div><a href="ratio_add.html" title="cpp/numeric/ratio/ratio add"><span class="t-lines"><span>ratio_add</span></span></a></div><div><span class="t-lines"><span><span class="t-mark-rev t-since-cxx11">(C++11)</span></span></span></div></div></td></tr>
<tr class="t-nv"><td colspan="5"><div class="t-nv-ln-table"><div><a href="ratio_subtract.html" title="cpp/numeric/ratio/ratio subtract"><span class="t-lines"><span>ratio_subtract</span></span></a></div><div><span class="t-lines"><span><span class="t-mark-rev t-since-cxx11">(C++11)</span></span></span></div></div></td></tr>
<tr class="t-nv"><td colspan="5"><div class="t-nv-ln-table"><div><a href="ratio_multiply.html" title="cpp/numeric/ratio/ratio multiply"><span class="t-lines"><span>ratio_multiply</span></span></a></div><div><span class="t-lines"><span><span class="t-mark-rev t-since-cxx11">(C++11)</span></span></span></div></div></td></tr>
<tr class="t-nv"><td colspan="5"><div class="t-nv-ln-table"><div><a href="ratio_divide.html" title="cpp/numeric/ratio/ratio divide"><span class="t-lines"><span>ratio_divide</span></span></a></div><div><span class="t-lines"><span><span class="t-mark-rev t-since-cxx11">(C++11)</span></span></span></div></div></td></tr>
<tr class="t-nv-h2"><td colspan="5"> 比较</td></tr>
<tr class="t-nv"><td colspan="5"><div class="t-nv-ln-table"><div><a href="ratio_equal.html" title="cpp/numeric/ratio/ratio equal"><span class="t-lines"><span>ratio_equal</span></span></a></div><div><span class="t-lines"><span><span class="t-mark-rev t-since-cxx11">(C++11)</span></span></span></div></div></td></tr>
<tr class="t-nv"><td colspan="5"><div class="t-nv-ln-table"><div><a href="ratio_not_equal.html" title="cpp/numeric/ratio/ratio not equal"><span class="t-lines"><span>ratio_not_equal</span></span></a></div><div><span class="t-lines"><span><span class="t-mark-rev t-since-cxx11">(C++11)</span></span></span></div></div></td></tr>
<tr class="t-nv"><td colspan="5"><div class="t-nv-ln-table"><div><a href="ratio_less.html" title="cpp/numeric/ratio/ratio less"><span class="t-lines"><span>ratio_less</span></span></a></div><div><span class="t-lines"><span><span class="t-mark-rev t-since-cxx11">(C++11)</span></span></span></div></div></td></tr>
<tr class="t-nv"><td colspan="5"><div class="t-nv-ln-table"><div><a href="ratio_less_equal.html" title="cpp/numeric/ratio/ratio less equal"><span class="t-lines"><span>ratio_less_equal</span></span></a></div><div><span class="t-lines"><span><span class="t-mark-rev t-since-cxx11">(C++11)</span></span></span></div></div></td></tr>
<tr class="t-nv"><td colspan="5"><div class="t-nv-ln-table"><div><a href="ratio_greater.html" title="cpp/numeric/ratio/ratio greater"><span class="t-lines"><span>ratio_greater</span></span></a></div><div><span class="t-lines"><span><span class="t-mark-rev t-since-cxx11">(C++11)</span></span></span></div></div></td></tr>
<tr class="t-nv"><td colspan="5"><div class="t-nv-ln-table"><div><a href="ratio_greater_equal.html" title="cpp/numeric/ratio/ratio greater equal"><span class="t-lines"><span>ratio_greater_equal</span></span></a></div><div><span class="t-lines"><span><span class="t-mark-rev t-since-cxx11">(C++11)</span></span></span></div></div></td></tr>
</table></div><div></div></div></div></div><div class="t-navbar-sep"> </div></div>
<table class="t-dcl-begin"><tbody>
<tr class="t-dsc-header">
<td> <div>定义于头文件 <code><a href="../../header/ratio.html" title="cpp/header/ratio">&lt;ratio&gt;</a></code>
 </div></td>
<td></td>
<td></td>
</tr>
<tr class="t-dcl t-since-cxx11">
<td> <div><span class="mw-geshi cpp source-cpp"><span class="kw1">template</span><span class="sy1">&lt;</span> <br>
<p>    <a href="../../types/integer.html"><span class="kw118">std::<span class="me2">intmax_t</span></span></a> Num, <br>
    <a href="../../types/integer.html"><span class="kw118">std::<span class="me2">intmax_t</span></span></a> Denom <span class="sy1">=</span> <span class="nu0">1</span> <br>
</p>
<span class="sy1">&gt;</span> <span class="kw1">class</span> ratio<span class="sy4">;</span></span></div></td>
<td class="t-dcl-nopad">  </td>
<td> <span class="t-mark-rev t-since-cxx11">(C++11 起)</span> </td>
</tr>
<tr class="t-dcl-sep"><td></td><td></td><td></td></tr>
</tbody></table>
<p>类模板 <code>std::ratio</code> 及相关的模板提供<a href="../ratio.html" title="cpp/numeric/ratio">编译时有理数算术支持</a>。此模板的每个实例化都准确表示任一确定有理数，只要分子 <code>Num</code> 与分母 <code>Denom</code> 能表示为 <span class="t-lc"><a href="../../types/integer.html" title="cpp/types/integer">std::intmax_t</a></span> 类型的编译时常量。另外， <code>Denom</code> 不可为零且不可等于最负的值。约分分子和分母到最简。
</p><p>静态数据成员 <code>num</code> 与 <code>den</code> 表示由将 <code>Num</code> 与 <code>Denom</code> 除以其最大公约数的分子与分母。然而，二个有相异的 <code>Num</code> 或 <code>Denom</code> 的 <code>std::ratio</code> 是不同的类型，即使它们表示同一有理数（在约分后）。能经由其 <code>type</code> 成员约分 <code>ratio</code> 类型到最简分数： <code>std::ratio&lt;3, 6&gt;::type</code> 为 <code>std::ratio&lt;1, 2&gt;</code> 。
</p><p>标准库提供数个对应 SI 比例的便利 typedef ：
</p>
<table class="t-dsc-begin">

<tr class="t-dsc-header">
<td colspan="2"> <div>定义于头文件 <code>&lt;ratio&gt;</code> </div>
</td></tr>

<tr class="t-dsc-sep">
<td colspan="2">  
</td></tr>
<tr class="t-dsc-hitem">
<td> 类型
</td>
<td> 定义
</td></tr>


<tr class="t-dsc">
<td>  <code>yocto</code>
</td>
<td>  <span class="t-c"><span class="mw-geshi cpp source-cpp">std<span class="sy4">::</span><span class="me2">ratio</span><span class="sy1">&lt;</span><span class="nu0">1</span>, <span class="nu0">1000000000000000000000000</span><span class="sy1">&gt;</span></span></span> ，若 <span class="t-lc"><a href="../../types/integer.html" title="cpp/types/integer">std::intmax_t</a></span> 能表示分母
</td></tr>

<tr class="t-dsc">
<td>  <code>zepto</code>
</td>
<td>  <span class="t-c"><span class="mw-geshi cpp source-cpp">std<span class="sy4">::</span><span class="me2">ratio</span><span class="sy1">&lt;</span><span class="nu0">1</span>, <span class="nu0">1000000000000000000000</span><span class="sy1">&gt;</span></span></span> ，若 <span class="t-lc"><a href="../../types/integer.html" title="cpp/types/integer">std::intmax_t</a></span> 能表示分母
</td></tr>

<tr class="t-dsc">
<td>  <code>atto</code>
</td>
<td>  <span class="t-c"><span class="mw-geshi cpp source-cpp">std<span class="sy4">::</span><span class="me2">ratio</span><span class="sy1">&lt;</span><span class="nu0">1</span>, <span class="nu0">1000000000000000000</span><span class="sy1">&gt;</span></span></span>
</td></tr>

<tr class="t-dsc">
<td>  <code>femto</code>
</td>
<td>  <span class="t-c"><span class="mw-geshi cpp source-cpp">std<span class="sy4">::</span><span class="me2">ratio</span><span class="sy1">&lt;</span><span class="nu0">1</span>, <span class="nu0">1000000000000000</span><span class="sy1">&gt;</span></span></span>
</td></tr>

<tr class="t-dsc">
<td>  <code>pico</code>
</td>
<td>  <span class="t-c"><span class="mw-geshi cpp source-cpp">std<span class="sy4">::</span><span class="me2">ratio</span><span class="sy1">&lt;</span><span class="nu0">1</span>, <span class="nu0">1000000000000</span><span class="sy1">&gt;</span></span></span>
</td></tr>

<tr class="t-dsc">
<td>  <code>nano</code>
</td>
<td>  <span class="t-c"><span class="mw-geshi cpp source-cpp">std<span class="sy4">::</span><span class="me2">ratio</span><span class="sy1">&lt;</span><span class="nu0">1</span>, <span class="nu0">1000000000</span><span class="sy1">&gt;</span></span></span>
</td></tr>

<tr class="t-dsc">
<td>  <code>micro</code>
</td>
<td>  <span class="t-c"><span class="mw-geshi cpp source-cpp">std<span class="sy4">::</span><span class="me2">ratio</span><span class="sy1">&lt;</span><span class="nu0">1</span>, <span class="nu0">1000000</span><span class="sy1">&gt;</span></span></span>
</td></tr>

<tr class="t-dsc">
<td>  <code>milli</code>
</td>
<td>  <span class="t-c"><span class="mw-geshi cpp source-cpp">std<span class="sy4">::</span><span class="me2">ratio</span><span class="sy1">&lt;</span><span class="nu0">1</span>, <span class="nu0">1000</span><span class="sy1">&gt;</span></span></span>
</td></tr>

<tr class="t-dsc">
<td>  <code>centi</code>
</td>
<td>  <span class="t-c"><span class="mw-geshi cpp source-cpp">std<span class="sy4">::</span><span class="me2">ratio</span><span class="sy1">&lt;</span><span class="nu0">1</span>, <span class="nu0">100</span><span class="sy1">&gt;</span></span></span>
</td></tr>

<tr class="t-dsc">
<td>  <code>deci</code>
</td>
<td>  <span class="t-c"><span class="mw-geshi cpp source-cpp">std<span class="sy4">::</span><span class="me2">ratio</span><span class="sy1">&lt;</span><span class="nu0">1</span>, <span class="nu0">10</span><span class="sy1">&gt;</span></span></span>
</td></tr>

<tr class="t-dsc">
<td>  <code>deca</code>
</td>
<td>  <span class="t-c"><span class="mw-geshi cpp source-cpp">std<span class="sy4">::</span><span class="me2">ratio</span><span class="sy1">&lt;</span><span class="nu0">10</span>, <span class="nu0">1</span><span class="sy1">&gt;</span></span></span>
</td></tr>

<tr class="t-dsc">
<td>  <code>hecto</code>
</td>
<td>  <span class="t-c"><span class="mw-geshi cpp source-cpp">std<span class="sy4">::</span><span class="me2">ratio</span><span class="sy1">&lt;</span><span class="nu0">100</span>, <span class="nu0">1</span><span class="sy1">&gt;</span></span></span>
</td></tr>

<tr class="t-dsc">
<td>  <code>kilo</code>
</td>
<td>  <span class="t-c"><span class="mw-geshi cpp source-cpp">std<span class="sy4">::</span><span class="me2">ratio</span><span class="sy1">&lt;</span><span class="nu0">1000</span>, <span class="nu0">1</span><span class="sy1">&gt;</span></span></span>
</td></tr>

<tr class="t-dsc">
<td>  <code>mega</code>
</td>
<td>  <span class="t-c"><span class="mw-geshi cpp source-cpp">std<span class="sy4">::</span><span class="me2">ratio</span><span class="sy1">&lt;</span><span class="nu0">1000000</span>, <span class="nu0">1</span><span class="sy1">&gt;</span></span></span>
</td></tr>

<tr class="t-dsc">
<td>  <code>giga</code>
</td>
<td>  <span class="t-c"><span class="mw-geshi cpp source-cpp">std<span class="sy4">::</span><span class="me2">ratio</span><span class="sy1">&lt;</span><span class="nu0">1000000000</span>, <span class="nu0">1</span><span class="sy1">&gt;</span></span></span>
</td></tr>

<tr class="t-dsc">
<td>  <code>tera</code>
</td>
<td>  <span class="t-c"><span class="mw-geshi cpp source-cpp">std<span class="sy4">::</span><span class="me2">ratio</span><span class="sy1">&lt;</span><span class="nu0">1000000000000</span>, <span class="nu0">1</span><span class="sy1">&gt;</span></span></span>
</td></tr>

<tr class="t-dsc">
<td>  <code>peta</code>
</td>
<td>  <span class="t-c"><span class="mw-geshi cpp source-cpp">std<span class="sy4">::</span><span class="me2">ratio</span><span class="sy1">&lt;</span><span class="nu0">1000000000000000</span>, <span class="nu0">1</span><span class="sy1">&gt;</span></span></span>
</td></tr>

<tr class="t-dsc">
<td>  <code>exa</code>
</td>
<td>  <span class="t-c"><span class="mw-geshi cpp source-cpp">std<span class="sy4">::</span><span class="me2">ratio</span><span class="sy1">&lt;</span><span class="nu0">1000000000000000000</span>, <span class="nu0">1</span><span class="sy1">&gt;</span></span></span>
</td></tr>

<tr class="t-dsc">
<td>  <code>zetta</code>
</td>
<td>  <span class="t-c"><span class="mw-geshi cpp source-cpp">std<span class="sy4">::</span><span class="me2">ratio</span><span class="sy1">&lt;</span><span class="nu0">1000000000000000000000</span>, <span class="nu0">1</span><span class="sy1">&gt;</span></span></span> ，若 <span class="t-lc"><a href="../../types/integer.html" title="cpp/types/integer">std::intmax_t</a></span> 能表示分子
</td></tr>

<tr class="t-dsc">
<td>  <code>yotta</code>
</td>
<td>  <span class="t-c"><span class="mw-geshi cpp source-cpp">std<span class="sy4">::</span><span class="me2">ratio</span><span class="sy1">&lt;</span><span class="nu0">1000000000000000000000000</span>, <span class="nu0">1</span><span class="sy1">&gt;</span></span></span> ，若 <span class="t-lc"><a href="../../types/integer.html" title="cpp/types/integer">std::intmax_t</a></span> 能表示分子
</td></tr>
</table>
<h3><span class="mw-headline" id=".E6.88.90.E5.91.98.E7.B1.BB.E5.9E.8B">成员类型</span></h3>
<table class="t-dsc-begin">

<tr class="t-dsc-sep">
<td colspan="2">  
</td></tr>
<tr class="t-dsc-hitem">
<td> 成员类型
</td>
<td> 定义
</td></tr>


<tr class="t-dsc">
<td>  <code>type</code>
</td>
<td>  <span class="t-c"><span class="mw-geshi cpp source-cpp">std<span class="sy4">::</span><span class="me2">ratio</span><span class="sy1">&lt;</span>num, den<span class="sy1">&gt;</span></span></span>
</td></tr>
</table>
<h3><span class="mw-headline" id=".E6.88.90.E5.91.98.E5.AF.B9.E8.B1.A1">成员对象</span></h3>
<table class="t-dsc-begin">

<tr class="t-dsc">
<td>  <div class="t-dsc-member-div"><div><span class="t-lines"><span><span class="t-dsc-small">constexpr intmax_t</span> num</span></span></div><div><span class="t-lines"><span><span class="t-cmark">[静态]</span></span></span></div></div>
</td>
<td>   <span class="t-lc"><a href="../../types/integer.html" title="cpp/types/integer">std::intmax_t</a></span> 类型的 <span class="t-c"><span class="mw-geshi cpp source-cpp"><span class="kw4">constexpr</span></span></span> 值，等于 <code>sign(Num) * sign(Denom) * abs(Num) / gcd(Num, Denom)</code>  <br> <span class="t-mark">(公开静态成员常量)</span>
</td></tr>

<tr class="t-dsc">
<td>  <div class="t-dsc-member-div"><div><span class="t-lines"><span><span class="t-dsc-small">constexpr intmax_t</span> den</span></span></div><div><span class="t-lines"><span><span class="t-cmark">[静态]</span></span></span></div></div>
</td>
<td>   <span class="t-lc"><a href="../../types/integer.html" title="cpp/types/integer">std::intmax_t</a></span> 类型的 <span class="t-c"><span class="mw-geshi cpp source-cpp"><span class="kw4">constexpr</span></span></span> 值，等于 <code>abs(Denom) / gcd(Num, Denom)</code>  <br> <span class="t-mark">(公开静态成员常量)</span>
</td></tr>
</table>

<!-- 
NewPP limit report
Preprocessor visited node count: 4811/1000000
Preprocessor generated node count: 9343/1000000
Post‐expand include size: 121759/2097152 bytes
Template argument size: 26038/2097152 bytes
Highest expansion depth: 15/40
Expensive parser function count: 0/100
-->

<!-- Saved in parser cache with key mwiki1-mwiki_zh_:pcache:idhash:3430-0!*!0!!*!*!zh!* and timestamp 20200221225619 -->
</div>                    <!-- /bodycontent -->
                                        <!-- printfooter -->
                    <div class="printfooter">
                    来自“<a href="https://zh.cppreference.com/mwiki/index.php?title=cpp/numeric/ratio/ratio&amp;oldid=62827">https://zh.cppreference.com/mwiki/index.php?title=cpp/numeric/ratio/ratio&amp;oldid=62827</a>”                    </div>
                    <!-- /printfooter -->
                                                            <!-- catlinks -->
                    <!-- /catlinks -->
                                                            <div class="visualClear"></div>
                    <!-- debughtml -->
                                        <!-- /debughtml -->
                </div>
                <!-- /bodyContent -->
            </div>
        </div>
        <!-- /content -->
        <!-- footer -->
        <div id="cpp-footer-base" class="noprint">
            <div id="footer">
                        <div id="cpp-navigation">
            <h5>导航</h5>
            <ul><li><a href="https://zh.cppreference.com/w/cpp/numeric/ratio/ratio">Online version</a></li><li>Offline version retrieved 2020-03-14 18:00.</li></ul></div>
                        <ul id="footer-info">
                                    <li id="footer-info-lastmod"> 本页面最后修改于2019年10月17日 (星期四) 00:31。</li>
                                    <li id="footer-info-viewcount">此页面已被浏览过6,795次。</li>
                            </ul>
                    </div>
        </div>
        <!-- /footer -->
        <script>if(window.mw){
mw.loader.state({"site":"loading","user":"missing","user.groups":"ready"});
}</script>
<script src="../../../../common/skin_scripts.js"></script>
<script>if(window.mw){
mw.loader.load(["mediawiki.action.view.postEdit","mediawiki.user","mediawiki.page.ready","mediawiki.searchSuggest","mediawiki.hidpi","ext.gadget.MathJax","ext.gadget.ColiruCompiler"], null, true);
}</script>
<script src="../../../../common/site_scripts.js"></script>
<script type="text/javascript">
var _gaq = _gaq || [];
_gaq.push(['_setAccount', 'UA-2828341-1']);
_gaq.push(['_setDomainName', 'cppreference.com']);
_gaq.push(['_trackPageview']);
</script><!-- Served in 1.785 secs. -->
	</body>
<!-- Cached 20200221225619 -->
</html>